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STATE PLANE COORDINATES Washington State Washington State Land Surveyors Association Larry Signani 13 March 2007

STATE PLANE COORDINATES Washington State Washington State Land Surveyors Association Larry Signani 13 March 2007. SURVEY TYPES. Surveys can be grouped into two categories: 1. Plane Surveys 2. Geodetic Surveys

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STATE PLANE COORDINATES Washington State Washington State Land Surveyors Association Larry Signani 13 March 2007

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  1. STATE PLANE COORDINATES Washington State Washington State Land Surveyors Association Larry Signani 13 March 2007

  2. SURVEY TYPES • Surveys can be grouped into two categories: • 1. Plane Surveys • 2. Geodetic Surveys A survey of a small area in which the area surveyed is considered flat except for topographic variations, is termed a plane survey and this branch of surveying is called Plane Surveying,. When a survey covers a large portion of the earth, the curvature of the earth has to be considered. Surveys of this type cannot be mapped on plane sheets of paper without distortions. These are called Geodetic Surveys, the position of points are indicated either by spherical coordinates , namely Latitude and Longitude, or by Plane Coordinates after projecting onto a plan surface, E.G., State Plane Coordinates

  3. SURVEY TYPES • Plane Surveys • assume earth’s surface is flat plane • use X-Y coordinates • easy procedures and computations • sufficient for most surveys • Geodetic Surveys • accurately represent earth’s shape • use spheroid coordinates (Latitude, Longitude) • more complex, expensive, difficult computations

  4. GEOCENTRIC AND GEOGRAPHICAL

  5. LATITUDE & LONGITUDE

  6. THE ELLIPSOIDMATHEMATICAL MODEL OF THE EARTH N b a S a = Semi major axis b = Semi minor axis f = a-b = Flattening a

  7. THE ELLIPSOID

  8. UNITED STATESELLIPSOID DEFINITIONS BESSEL 1841 a = 6,377,397.155 m 1/f = 299.1528128 CLARKE 1866 a = 6,378,206.4 m 1/f = 294.97869821 GEODETIC REFERENCE SYSTEM 1980 - (GRS 80) a = 6,378,137 m 1/f = 298.257222101 WORLD GEODETIC SYSTEM 1984 - (WGS 84) a = 6,378,137 m 1/f =298.257223563

  9. THE ELLIPSOID (1738)6,397,3006,363,806.283191FranceEverest (1830)6,377,563.3966,356,256.909299.3249646BritainBessel (1866)6,378,206.46,356,583.8294.9786982North AmericaClarke (1880)6,378,249.1456,356,514.870293.465France, AfricaHelmert (1969)6,378,1606,356,774.719298.25South AmericaWGS-72 (1972)6,378,1356,356,750.52298.26USA/DoDGRS-80 (1979)6,378,1376,356,752.3141298.257222101NAD 83 (1982)6,378,1376,356,752.3298.257024899N AmericaWGS-84 (2003)6,378,136.66,356,751.9298.25642Global ITRS

  10. THE GEOID AND TWO ELLIPSOIDS CLARKE 1866 GRS80-WGS84 Earth Mass Center Approximately 236 meters GEOID

  11. DATUMS • A set of constants specifying the coordinate system used for geodetic control, i.e., for calculating coordinates of points on the Earth. Specific geodetic datums are usually given distinctive names. (e.g., North American Datum of 1983, European Datum 1950, National Geodetic Vertical Datum of 1929)

  12. DATUM

  13. VERTICAL DATUMS • MEAN SEA LEVEL DATUM OF 1929 • NATIONAL GEODETIC VERTICAL DATUM OF 1929 • (As of July 2, 1973) • NORTH AMERICAN VERTICAL DATUM OF 1988 • (As of June 24, 1993)

  14. NGVD 29 and NAVD 88

  15. COMPARISON OF VERTICAL DATUM ELEMENTS • NGVD 29NAVD 88 • DATUM DEFINITION 26 TIDE GAUGES FATHER’S POINT/RIMOUSKI • IN THE U.S. & CANADA QUEBEC, CANADA • BENCH MARKS 100,000 450,000 • LEVELING (Km) 102,724 1,001,500 • GEOID FITTING Distorted to Fit MSL Gauges Best Continental Model

  16. COMPARISON OF DATUM ELEMENTS • NAD 27NAD 83 • ELLIPSOID CLARKE 1866 GRS80 • a = 6,378,206.4 m a = 6,378,137. M • 1/f = 294.9786982 1/f = 298.257222101 • DATUM POINT Triangulation Station NONE • MEADES RANCH, KANSAS EARTH MASS CENTER • ADJUSTMENT 25k STATIONS 250k STATIONS • Several Hundred Base Lines Appox. 30k EDMI Base Lines • Several Hundred Astro Azimuths 5k Astro Azimuths • Doppler Point Positions • VLBI Vectors • BEST FITTING North America World-Wide

  17. NAD 27 and NAD 83

  18. HIGH ACCURACY REFERENCE NETWORKS • “GPSABLE” • Clear Horizons for Satellite Signal Acquisition • EASY ACCESSIBILITY • Few Special Vehicle or Property Entrance Requirements • REGULARLY SPACED • Always within 20-100 Km • HIGH HORIZONTAL ACCURACY • A-Order (5 mm + 1:10,000,000) • B-Order (8mm + 1:1,000,000)

  19. HIGH ACCURACY REFERENCE NETWORKS

  20. HARN

  21. HARN

  22. THE GEOID

  23. GRID AZIMUTH COMPUTATION • ag = aA + Laplace Correction - g • = 253o 26’ 14.9” (Observed Astro Azimuth) • + (- 0.1)” (Laplace Correction) • = 253o 26’ 14.8” (Geodetic Azimuth) • - 0 36 37.0 (Convergence Angle) • = 252o 49’ 37.8” • The convention of the sign of the convergence angle is • always from Grid to Geodetic

  24. UNDULATIONS OF THE GEOID

  25. UNDULATIONS OF THE GEOID

  26. ELLIPSOID - GEOID RELATIONSHIP H = Orthometric Height(NAVD 88) h = Ellipsoidal Height (NAD 83) H =h -N N = Geoid Height (GEOID 99) H TOPOGRAPHIC SURFACE h N GEOID99 Geoid PERPENDICULAR TO ELLIPSOID Ellipsoid GRS80 PERPENDICULAR TO GEOID (PLUMBLINE) DEFLECTION OF THE VERTICAL DEFLEC99

  27. State Plane Coordinates BRIEF HISTORY: -Originally a U.S. English unit grid system -Developed by land surveyors in the 1930’s to simplify surveying computations cooperative venture between the Coast and Geodetic Survey and the North Carolina state government, and efforts to build a North Carolina spatial coordinate system with minimal distortion was started. In 1933 this cooperative venture produced the North Carolina Coordinate System. In less that 12 months, the North Carolina system had been copied into all of the remaining states, and the State Plane coordinate system was born. -Used only in the US

  28. STATE PLANE COORDINATE SYSTEMS • Lambert Conformal Conic and Transverse Mercator Projections • International, State and County Boundaries • NAD 27 - Coordinates in U.S. Survey Feet • NAD 83 - Coordinates Metric w/State Defined Foot Conversion • 1 Meter = 3.280833333 U.S. Survey Feet • 1 Meter = 3.280839895 International Feet • NAD 27 to NAD 83 VERY large Positional Shifts

  29. Types of Plane Systems Pointof Origin Plane Apex ofCone Ellipsoid Axis of Cone & Ellipsoid Axis of Ellipsoid Tangent Plane Local Plane Standard Parallels Axis of Cylinder Ellipsoid Ellipsoid Intersecting Cylinder Transverse Mercator Intersecting Cone 2 Parallel Lambert

  30. LAMBERT CONFROMAL CONICWITH 2 STANDARD PARALLELS STANDARD PARALLELS Approximately 158 miles 80 CENTRAL MERIDIAN

  31. d’ GEODETIC vs. GRID DISTANCE c’ d c cd < c’d’ b b’ ab > a’b’ a a’ Earth Center

  32. LAMBERT CONFROMAL CONICWITH 2 STANDARD PARALLELS Grid Scale Factor SCALE > 1 Nn SCALE EXACT STANDARD PARALLELS SCALE < 1 Ns SCALE EXACT SCALE > 1 80 CENTRAL MERIDIAN

  33. Standard Parallels

  34. TRANSVERSE MERCATOR SCALE < 1 SCALE > 1 SCALE > 1 SCALE EXACT SCALE EXACT 80 CENTRAL MERIDIAN

  35. STATE PLANE COORDINATE SYSTEMS

  36. North and South Zones 48-44 47-30 47-20 N. Zone Origin 47-00/120-50 N=0m, E=500,000m 45-50 S. Zone Origin 45-20/120-30 N=0m, E=500,000m

  37. WASHINGTON ZONES

  38. PARAMETERS OF A LAMBERT PROJECTION

  39. RCW 58.20 • RCW 58.20.110 • Definitions. • Unless the context clearly requires otherwise, the definitions in this section apply throughout RCW 58.20.110 through 58.20.220 and 58.20.901:     (1) "Committee" means the interagency federal geodetic control committee or its successor;     (2) "GRS 80" means the geodetic reference system of 1980 as adopted in 1979 by the international union of geodesy and geophysics defined on an equipotential ellipsoid;     (3) "National geodetic survey" means the national ocean service's national geodetic survey of the national oceanic and atmospheric administration, United States department of commerce, or its successor;     (4) "Washington coordinate system of 1927" means the system of plane coordinates in effect under this chapter until July 1, 1990, which is based on the North American datum of 1927 as determined by the national geodetic survey of the United States department of commerce;     (5) "Washington coordinate system of 1983" means the system of plane coordinates under this chapter based on the North American datum of 1983 as determined by the national geodetic survey of the United States department of commerce. • [1989 c 54 § 9.]

  40. RCW 58.20 • RCW 58.20.120 • System designation — Permitted uses. • Until July 1, 1990, the Washington coordinate system of 1927, or its successor, the Washington coordinate system of 1983, may be used in Washington for expressing positions or locations of points on the surface of the earth. On and after that date, the Washington coordinate system of 1983 shall be the designated coordinate system in Washington. The Washington coordinate system of 1927 may be used only for purposes of reference after June 30, 1990.

  41. RCW 58.20 • RCW 58.20.130 • Plane coordinates adopted — Zones. • The system of plane coordinates which has been established by the national geodetic survey for defining and stating the positions or locations of points on the surface of the earth within the state of Washington is designated as the "Washington coordinate system of 1983."     For the purposes of this system the state is divided into a "north zone" and a "south zone."     The area now included in the following counties shall constitute the north zone: Chelan, Clallam, Douglas, Ferry, Island, Jefferson, King, Kitsap, Lincoln, Okanogan, Pend Oreille, San Juan, Skagit, Snohomish, Spokane, Stevens, Whatcom, and that part of Grant lying north of parallel 47° 30' north latitude.     The area now included in the following counties shall constitute the south zone: Adams, Asotin, Benton, Clark, Columbia, Cowlitz, Franklin, Garfield, that part of Grant lying south of parallel 47° 30' north latitude, Grays Harbor, Kittitas, Klickitat, Lewis, Mason, Pacific, Pierce, Skamania, Thurston, Wahkiakum, Walla Walla, Whitman and Yakima.

  42. RCW 58.20 • RCW 58.20.150 • Designation of coordinates — "N" and "E." • "N" and "E" shall be used in labeling coordinates of a point on the earth's surface and in expressing the position or location of such point relative to the origin of the appropriate zone of this system, expressed in meters and decimals of a meter. These coordinates shall be made to depend upon and conform to the coordinates, on the Washington coordinate system of 1983, of the horizontal control stations of the national geodetic survey within the state of Washington, as those coordinates have been determined, accepted, or adjusted by the survey.

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